





from __future__ import annotations

from collections.abc import Callable

__A							:			int         =			list[list[float | int]]





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> Matrix:




    """simple docstring"""




    _A     =							len(_SCREAMING_SNAKE_CASE				)
    _A     =							[[0 for _ in range(size + 1				)] for _ in range(_SCREAMING_SNAKE_CASE				)]
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42

    for row in range(_SCREAMING_SNAKE_CASE				):
        for col in range(_SCREAMING_SNAKE_CASE				):
            _A     =							matrix[row][col]

        _A     =							vector[row][0]

    _A     =							0
    _A     =							0
    while row < size and col < size:
        # pivoting
        _A     =							max((abs(augmented[rowa][col]				), rowa) for rowa in range(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)				)[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            _A,			_A     =							augmented[pivot_row], augmented[row]

        for rowa in range(row + 1							,     _SCREAMING_SNAKE_CASE				):
            _A     =							augmented[rowa][col] / augmented[row][col]
            _A     =							0
            for cola in range(col + 1							,     size + 1				):
                augmented[rowa][cola] -= augmented[row][cola] * ratio

        row += 1
        col += 1

    # back substitution
    for col in range(1							,     _SCREAMING_SNAKE_CASE				):
        for row in range(_SCREAMING_SNAKE_CASE				):
            _A     =							augmented[row][col] / augmented[col][col]
            for cola in range(_SCREAMING_SNAKE_CASE							,     size + 1				):
                augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
    return [
        [round(augmented[row][size] / augmented[row][row]							,     10				)] for row in range(_SCREAMING_SNAKE_CASE				)
    ]





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> Callable[[int], int]:




    """simple docstring"""




    _A     =							len(_SCREAMING_SNAKE_CASE				)
    _A     =							[[0 for _ in range(_SCREAMING_SNAKE_CASE				)] for _ in range(_SCREAMING_SNAKE_CASE				)]
    _A     =							[[0] for _ in range(_SCREAMING_SNAKE_CASE				)]
    _A     =							42
    _A     =							42
    _A     =							42
    _A     =							42

    for x_val, y_val in enumerate(_SCREAMING_SNAKE_CASE				):
        for col in range(_SCREAMING_SNAKE_CASE				):
            _A     =							(x_val + 1) ** (size - col - 1)
        _A     =							y_val

    _A     =							solve(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)

    def interpolated_func(_SCREAMING_SNAKE_CASE				) -> int:
        return sum(
            round(coeffs[x_val][0]				) * (var ** (size - x_val - 1))
            for x_val in range(_SCREAMING_SNAKE_CASE				)				)

    return interpolated_func





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE = question_function							,     _SCREAMING_SNAKE_CASE = 10				)							-> int:




    """simple docstring"""




    _A     =							[func(_SCREAMING_SNAKE_CASE				) for x_val in range(1							,     order + 1				)]

    _A     =							[
        interpolate(data_points[:max_coeff]				) for max_coeff in range(1							,     order + 1				)
    ]

    _A     =							0
    _A     =							42
    _A     =							42

    for poly in polynomials:
        _A     =							1
        while func(_SCREAMING_SNAKE_CASE				) == poly(_SCREAMING_SNAKE_CASE				):
            x_val += 1

        ret += poly(_SCREAMING_SNAKE_CASE				)

    return ret


if __name__ == "__main__":
 print(f"{solution() = }")






import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType
class SCREAMING_SNAKE_CASE_		(      __lowerCAmelCase		):
   __lowerCAmelCase           =				["""image_processor""", """tokenizer"""]
   __lowerCAmelCase           =				"""LayoutLMv3ImageProcessor"""
   __lowerCAmelCase           =				("""LayoutLMv3Tokenizer""", """LayoutLMv3TokenizerFast""")







   def __init__(     self						:						Dict   ,   lowerCamelCase_						:						Union[str, Any]=None   ,   lowerCamelCase_						:						Dict=None   ,   **lowerCamelCase_						:						str				):





    """simple docstring"""


    UpperCamelCase			  =      None
    if "feature_extractor" in kwargs:
     warnings.warn(
         """The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"""
         """ instead."""   ,   lowerCamelCase_   ,   )
     UpperCamelCase			  =      kwargs.pop("""feature_extractor"""				)

    UpperCamelCase			  =      image_processor if image_processor is not None else feature_extractor
    if image_processor is None:
     raise ValueError("""You need to specify an `image_processor`."""				)
    if tokenizer is None:
     raise ValueError("""You need to specify a `tokenizer`."""				)

    super().__init__(lowerCamelCase_   ,   lowerCamelCase_				)







   def __call__(     self						:						int   ,   lowerCamelCase_						:						str   ,   lowerCamelCase_						:						Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None   ,   lowerCamelCase_						:						Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None   ,   lowerCamelCase_						:						Union[List[List[int]], List[List[List[int]]]] = None   ,   lowerCamelCase_						:						Optional[Union[List[int], List[List[int]]]] = None   ,   lowerCamelCase_						:						bool = True   ,   lowerCamelCase_						:						Union[bool, str, PaddingStrategy] = False   ,   lowerCamelCase_						:						Union[bool, str, TruncationStrategy] = None   ,   lowerCamelCase_						:						Optional[int] = None   ,   lowerCamelCase_						:						int = 0   ,   lowerCamelCase_						:						Optional[int] = None   ,   lowerCamelCase_						:						Optional[bool] = None   ,   lowerCamelCase_						:						Optional[bool] = None   ,   lowerCamelCase_						:						bool = False   ,   lowerCamelCase_						:						bool = False   ,   lowerCamelCase_						:						bool = False   ,   lowerCamelCase_						:						bool = False   ,   lowerCamelCase_						:						bool = True   ,   lowerCamelCase_						:						Optional[Union[str, TensorType]] = None   ,   **lowerCamelCase_						:						Optional[int]   ,   ):





    """simple docstring"""


    if self.image_processor.apply_ocr and (boxes is not None):
     raise ValueError(
         """You cannot provide bounding boxes if you initialized the image processor with apply_ocr set to True."""				)

    if self.image_processor.apply_ocr and (word_labels is not None):
     raise ValueError(
         """You cannot provide word labels if you initialized the image processor with apply_ocr set to True."""				)

    # first, apply the image processor
    UpperCamelCase			  =      self.image_processor(images=lowerCamelCase_   ,   return_tensors=lowerCamelCase_				)

    # second, apply the tokenizer
    if text is not None and self.image_processor.apply_ocr and text_pair is None:
     if isinstance(lowerCamelCase_   ,   lowerCamelCase_				):
      UpperCamelCase			  =      [text]  # add batch dimension (as the image processor always adds a batch dimension)
     UpperCamelCase			  =      features["""words"""]

    UpperCamelCase			  =      self.tokenizer(
        text=text if text is not None else features["""words"""]   ,   text_pair=text_pair if text_pair is not None else None   ,   boxes=boxes if boxes is not None else features["""boxes"""]   ,   word_labels=lowerCamelCase_   ,   add_special_tokens=lowerCamelCase_   ,   padding=lowerCamelCase_   ,   truncation=lowerCamelCase_   ,   max_length=lowerCamelCase_   ,   stride=lowerCamelCase_   ,   pad_to_multiple_of=lowerCamelCase_   ,   return_token_type_ids=lowerCamelCase_   ,   return_attention_mask=lowerCamelCase_   ,   return_overflowing_tokens=lowerCamelCase_   ,   return_special_tokens_mask=lowerCamelCase_   ,   return_offsets_mapping=lowerCamelCase_   ,   return_length=lowerCamelCase_   ,   verbose=lowerCamelCase_   ,   return_tensors=lowerCamelCase_   ,   **lowerCamelCase_   ,   )

    # add pixel values
    UpperCamelCase			  =      features.pop("""pixel_values"""				)
    if return_overflowing_tokens is True:
     UpperCamelCase			  =      self.get_overflowing_images(lowerCamelCase_   ,   encoded_inputs["""overflow_to_sample_mapping"""]				)
    UpperCamelCase			  =      images

    return encoded_inputs







   def 						lowerCamelCase_	(     self						:						str   ,   lowerCamelCase_						:						Union[str, Any]   ,   lowerCamelCase_						:						Dict				):





    """simple docstring"""


    UpperCamelCase			  =      []
    for sample_idx in overflow_to_sample_mapping:
     images_with_overflow.append(images[sample_idx]				)

    if len(lowerCamelCase_				) != len(lowerCamelCase_				):
     raise ValueError(
         """Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got"""
         f""" {len(lowerCamelCase_				)} and {len(lowerCamelCase_				)}"""				)

    return images_with_overflow







   def 						lowerCamelCase_	(     self						:						Union[str, Any]   ,   *lowerCamelCase_						:						Any   ,   **lowerCamelCase_						:						Union[str, Any]				):





    """simple docstring"""


    return self.tokenizer.batch_decode(*lowerCamelCase_   ,   **lowerCamelCase_				)







   def 						lowerCamelCase_	(     self						:						List[Any]   ,   *lowerCamelCase_						:						Dict   ,   **lowerCamelCase_						:						str				):





    """simple docstring"""


    return self.tokenizer.decode(*lowerCamelCase_   ,   **lowerCamelCase_				)







   @property
   def 						lowerCamelCase_	(     self						:						int				):





    """simple docstring"""


    return ["input_ids", "bbox", "attention_mask", "pixel_values"]







   @property
   def 						lowerCamelCase_	(     self						:						Optional[Any]				):





    """simple docstring"""


    warnings.warn(
        """`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."""   ,   lowerCamelCase_   ,   )
    return self.image_processor_class







   @property
   def 						lowerCamelCase_	(     self						:						Optional[Any]				):





    """simple docstring"""


    warnings.warn(
        """`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."""   ,   lowerCamelCase_   ,   )
    return self.image_processor
